It is important to convey the idea that the vigilantes protect the innocent, and they persist/persevere with their pursuit of the abusers or murderers until retribution has been exacted. For literary reasons, I would like both English and Latin versions to start with the letter "p".

Unfortunately, I have not taken any instruction in Latin, so I am relying on the expertise of others to help me with this.

I'm not sure that protego can be used without an object. It's a bit like writing in English "we cover" -- cover what? the reader is left asking. But then for all I know such things may be allowed in mottoes for the sake of brevity. Personally, I would read nos protegimus as 'we protect ourselves'.

I suppose the word persistimus must exist -- it certainly looks plausible --, but it is not in the Oxford Latin Dictionary, so it might be best to go with perstamus or maybe perseveramus.